1. The problem statement, all variables and given/known data Consider the function f(y,y',x) = 2yy' + 3x2y where y(x) = 3x4 - 2x +1. Compute ∂f/∂x and df/dx. Write both solutions of the variable x only. 2. Relevant equations Euler Equation: ∂f/∂y - d/dx * ∂f/∂y' = 0 3. The attempt at a solution Would I first just find ∂f/∂y and ∂f/∂y' as follows: ∂f/∂y = 2y' + 3x2 ∂f/∂y' = 2y and then insert y(x) and y'(x) into my two equations for ∂f/∂y and ∂f/∂y': y(x) = 3x4 - 2x +1 y'(x) = 12x3 - 2 → ∂f/∂y = 2(12x3 - 2) + 3x2 → ∂f/∂y' = 2(3x4 - 2x +1) This is where I begin to get lost. Would I plug these values into my Euler equation to find an expression for df/dx and ∂f/∂x? I would attempt this but I want to see if I'm headed in the right direction or not first. Any help would be much appreciated.